Refractive index mu is given as `mu=A+B/lambda^2,` where A and B are constants and lambda is wavelength, then dimensions of B are same as that of

Options

A. wavelength
B. volume
C. pressure
D. area

Explanation

To find the dimensions of the constant \( B \) in the given refractive index equation \( \mu = A + \frac{B}{\lambda^2} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The refractive index \( \mu \) is given by the equation:
\[ \mu = A + \frac{B}{\lambda^2} \]
Here, \( A \) and \( B \) are constants, and \( \lambda \) is the wavelength.

2. **Identify the Nature of Refractive Index**: The refractive index \( \mu \) is a dimensionless quantity. This means that it has no units and can be expressed as:
\[ [\mu] = M^0 L^0 T^0 \]

3. **Determine the Dimensions of \( A \)**: Since \( \mu \) is dimensionless and \( A \) is added to \( \frac{B}{\lambda^2} \), \( A \) must also be dimensionless:
\[ [A] = M^0 L^0 T^0 \]

4. **Analyze the Term \( \frac{B}{\lambda^2} \)**: The term \( \frac{B}{\lambda^2} \) must also be dimensionless because it is added to \( A \) (which is dimensionless). Therefore, we can write:
\[ \frac{[B]}{[\lambda]^2} = M^0 L^0 T^0 \]

5. **Determine the Dimensions of Wavelength \( \lambda \)**: The wavelength \( \lambda \) has dimensions of length:
\[ [\lambda] = L \]

6. **Substituting the Dimensions of \( \lambda \)**: Now substitute the dimensions of \( \lambda \) into the equation:
\[ \frac{[B]}{L^2} = M^0 L^0 T^0 \]

7. **Solving for Dimensions of \( B \)**: To find the dimensions of \( B \), we can rearrange the equation:
\[ [B] = L^2 \cdot M^0 L^0 T^0 = L^2 \]

8. **Conclusion**: The dimensions of \( B \) are:
\[ [B] = L^2 \]

### Final Answer:
The dimensions of \( B \) are the same as that of area, which is \( L^2 \).